Hmm, I can duplicate this issue. But investigating it more, it is not strictly a psycopg2 issue, either.
As Levente noted, the installers use Windows registry keys to determine the location of the Python installation. Between python 3.4.x and 3.5.x, it looks like the registry key for 32bit Python was changed from a format of 3.5 to 3.5-32.
This change causes a problem for ALL 32bit extension installers on Python 3.5 that use the standard Python stub installer.
Briefly looking at the stub code, I believe the standard Python stub installer only recognizes registry keys in the format <major>.<minor>. The extra '-32' at the end of the registry key makes the installer ignore the key, never finding the Python installation.
Another package that uses the Python stub installer, pycurl, exhibits the same issues:
I'm not suggesting this, but a workaround is to rename the following registry key from:
SOFTWARE\WOW6432Node\Python\PythonCore\3.5-32
SOFTWARE\WOW6432Node\Python\PythonCore\3.5
(ie, remove the '-32')
Install the extension, and then rename the registry back. Don't forget to rename it back!
Another workaround is to use the 64bit version of Python and Extensions.
-jason